Method and apparatus for measuring optical power of very weak light, and optical communication system using the same

ABSTRACT

A method and apparatus for measuring the optical power of very weak light arriving at a receiver, by using a photon detector, are provided. A photon detector detects the presence or absence of the arrival of a photon in accordance with bias application timing. For a train of optical pulses coming in at an arbitrary timing in respective time slots, the bias application timing is sequentially shifted within the range of a time slot. Each time a shift is made, the number of photons detected is counted by a photon counter. Based on this number of photons, the optical power of the train of the optical pulses is measured.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to techniques of measuring the opticalpower of light and, more particularly, to a method and apparatus formeasuring the optical power of very weak light and an opticalcommunication system using the method.

2. Description of the Related Art

In the field of optical communications, in recent years, active studieshave been devoted to quantum key distribution systems, which areregarded as realizing the high secrecy along a transmission line, and avariety of proposals have been made in regard to the systems.

As a basic one of the systems, a system which allows a sender and areceiver to share a quantum cryptographic key by using two types ofbases is proposed in Bennett and brassard, “QUANTUM CRYPTOGRAPHY, PUBLICKEY DISTRIBUTION AND COIN TOSSING” IEEE International Conference onComputers, Systems, and Signal Processing, Bangalore, India, pp.175-179. According to this proposal, the sender phase-modulates a photonby using any one of four kinds of information according to thecombinations of two bases (D, R) each representing quantum states, andbinary random data (0, 1), and then transmits the phase-modulated photonto the receiver. The receiver receives the photon by using the bases (D,R) independently of the sender and stores the reception data.Thereafter, the sender and receiver use an ordinary channel to checkwhether or not the bases used in transmission and the bases used inreception are the same, and determine final shared secret data basedonly on the reception data corresponding to the matching bases.

A plug and play quantum key distribution system proposed by a team ofthe University of Geneva, Switzerland (see G. Ribordy, “Automated ‘plug& play’ quantum key distribution”, Electronics Letters, Vol. 34, No. 22,PP. 2116-2117) is thought of as a promising scheme for bringingpolarization-sensitive quantum key distribution systems into practicaluse, because this system can compensate for the fluctuation inpolarization occurring along an optical fiber transmission line. Aschematic configuration of a plug and play system is shown in FIG. 1.

As shown in FIG. 1, in the plug and play system, a receiver, the one toreceive a quantum cryptographic key, is provided with a laser LD, whichgenerates optical pulses P. An optical pulse P is split into two partsat an optical coupler, and one of the two parts, an optical pulse P1,passes along a short path, whereas the other one, an optical pulse P2,passes along a long path. The pulses P1 and P2 are transmitted to asender as double pulses.

The sender is provided with a Faraday mirror and a phase modulator A.The received optical pulses P1 and P2 are reflected by the Faradaymirror individually, whereby they are sent back to the receiver withtheir polarization states rotated by 90 degrees. In this event, thephase modulator A phase-modulates the optical pulse P2 at the timingwhen the optical pulse P2 is passing through the phase modulator A. Thephase-modulated optical pulse P2*^(a) is returned to the receiver.

Since the polarization state of each of the optical pulses P1 andP2*^(a) received from the sender has been rotated by 90 degrees, apolarization beam splitter PBS in the receiver leads each of thesereceived pulses into the other path that is different from the path thepulse used when it was transmitted to the sender. Specifically, thereceived optical pulse P1 is led into the long path and phase-modulatedat the timing when it is passing through a phase modulator B, and thephase-modulated optical pulse P1*^(b) arrives at the optical coupler. Onthe other hand, the optical pulse P2*^(a), which has beenphase-modulated at the sender, passes along the short path, which isdifferent from the path it used when transmitted to the sender, and thenarrives at the same optical coupler. Accordingly, the optical pulseP2*^(a), phase-modulated on the sender side, and the optical pulseP1*^(b), phase-modulated on the receiver side, interfere with eachother, and the result of this interference is detected by a photondetector APD0 or APD1. Note that avalanche photodiodes are used as thephoton detectors, which are driven in a gated Geiger mode (GGM).

As described above, one optical pulse generated at the receiver is splitinto two, and the thus obtained double pulses P1 and P2 each have around-trip between the receiver and sender while being phase-modulatedindividually. As a whole, the two pulses pass along the same opticalpath and then interfere with each other. Accordingly, the result of theinterference observed by the photon detector APD0 or APD1, in whichvariations in delay due to an optical fiber transmission line arecancelled out, depends on the difference between the amount of a phasemodulation at the sender and the amount of a phase modulation at thereceiver.

A plug and play system having such a configuration requiressynchronization as cited below.

(1) In the sender, it is necessary to apply a voltage corresponding tothe amount of a phase modulation to the phase modulator A synchronouslywith the timing when the optical pulse P2 transmitted from the receiveris passing through the phase modulator A.

(2) In the receiver, it is necessary to apply a voltage corresponding tothe amount of a phase modulation to the phase modulator B synchronouslywith the timing when the optical pulse P1 returned from the sender ispassing through the phase modulator B.

(3) Further in the receiver, it is necessary to apply bias to the photondetectors APD0 and APD1 synchronously with the timing of the incidenceof the returned pulse (supersensitive reception in the gated Geigermode).

As described above, for a quantum key distribution system to stablygenerate a quantum cryptographic key by achieving high interference inpractice, it is indispensable to perform such timing control that thephase modulator A on the sender side and the phase modulator B andphoton detectors APD on the receiver side are each driven synchronouslywith the timing of the arrival of an optical pulse.

In the case of a system that transmits information by utilizing phasemodulation such as the above-described quantum key distribution system,it cannot be determined whether or not the timing of driving the phasemodulator A at the sender is right, unless the result of theinterference observed by the photon detector APD0 or APD1 on thereceiver side is referred to. Accordingly, in order to accuratelyperform the above-mentioned timing control, it is necessary toaccurately know the extinction ratio of the interferometer (the ratiobetween the optical powers observed by the photon detectors APD0 andAPD1) at the receiver.

However, in the case of the gated-Geiger-mode reception, bias is appliedto a photon detector APD only for a predetermined period of time, at thetiming of the arrival of an optical pulse. If a photon arrives while thegate voltage is being applied, the photon detector APD is broken down,and multiplication current continues to flow until the application ofgate voltage is finished. Therefore, what can be detected by the photondetector is, except a noise, merely whether or not a photon arrivesduring the gate voltage application, and the extinction ratio, which isobtained based on the time average of photon detections, cannot bemeasured.

Therefore, it has been conventionally necessary that, each timetransmission paths are changed, the extinction ratio be measured byusing, for example, optical power measurement equipment in place of thephoton detectors APD and then the timing of applying voltage to thephase modulator at the sender be determined. In other words, it has beennecessary to provide the receiver with both the optical powermeasurement equipment for determining the sender's driving timing andthe photon detectors APD for quantum cryptographic key generation.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a method and apparatusfor measuring the optical power of very weak light by using a photondetector.

Another object of the present invention is to provide an opticalcommunication system that optimizes the timing in the sender by usingthe weak-light power measurement method and thus enables information tobe stably transmitted at right timing.

Still another object of the present invention is to provide an opticalcommunication system that drives the phase modulator on the sender sideat right timing and thus enables high-speed, stable quantum keydistribution.

According to the present invention, the optical power of a series ofoptical pulses can be measured by using a photon detector for detectingphoton arrival according to driving timing. The optical power of aseries of optical pulses can be measured based on the number of photonscounted by shifting the driving timing.

In an optical communication system according to the present invention, afirst communication device includes: a modulator for modulating a seriesof optical pulses according to original information to be transmitted,at given modulation timing to transmit the series of modulated opticalpulses to a second communication device through a first communicationchannel; and a timing supplier for supplying the modulation timing tothe modulator, wherein the modulation timing is changeable. The secondcommunication device includes: a photon detector for detecting photonarrival of the series of optical pulses through the firstcommunication-channel according to driving timing; a counter forcounting a number of photons detected by the photon detector; ameasurement section for measuring optical power of the series of opticalpulses based on the number of photons counted by shifting the drivingtiming; and a timing controller for controlling the modulation timing ofthe first communication device through a second communication channelbased on the optical power measured by the measurement section.

As described above, according to the present invention, by shifting thephase of driving timing at which a bias voltage is applied to a photondetector, a photon counter counts the number of photons which havearrived for a period of time during which the bias voltage is applied tothe photon detector. Assuming that the wavelength of optical pulses isknown, the optical power of the optical pulses can be obtained from thenumber of counted photons. Accordingly, a photon detector can be used tomeasure the optical power or similar physical quantity of very weaklight.

Since the optical power or similar physical quantity of very weak lightcan be measured by a photon detector in the above manner, an opticaltransmitter in an optical communication system can be operated atoptimal timing, resulting in stable information transmission. In thecase of the present invention being applied to a quantum keydistribution system, a phase modulator at a transmitting side can beoperated at right timing, resulting in high-speed and stable quantum keydistribution.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a schematic configuration of a plugand play system.

FIG. 2 is a block diagram showing a schematic configuration of aweak-light power measurement apparatus according to a mode of thepresent invention.

FIG. 3 is a waveform diagram for describing the states of phase shiftsfor bias application timing, in a weak-light power measurement methodaccording to this mode.

FIG. 4 is a graph schematically showing a photon count varying with theamount of a phase shift.

FIG. 5 is a block diagram showing a configuration of atemperature-independent plug and play system according to a firstembodiment of the present invention.

FIG. 6 is a schematic configuration diagram for describing the operationof a PBS loop at a sender.

FIG. 7 is an explanatory diagram showing a time sequence of opticalpulses propagating through the PBS loop.

FIG. 8 is a flowchart showing a sender's timing search, including aprocedure of measuring an extinction ratio at a receiver, in the systemaccording to the first embodiment of the present invention.

FIG. 9 is a handshake diagram showing a sequence of the control of thesender's timing, in which parts (a) to (d) correspond to fourcombinations of a basis and a random number, respectively.

FIGS. 10A to 10D are graphs corresponding to the four combinations of abasis and a random number, respectively, each showing variations in theeffective photon counts and extinction ratio measured at the receiver.

FIG. 11 is a diagram schematically showing a data table of the effectivephoton counts of the photon detectors APD0 and APD1 and the amounts ofthe clock shift, stored in a memory 270.

FIG. 12 is a flowchart showing a procedure of the control of thesender's timing, in a quantum cryptographic system according to a secondembodiment of the present invention.

FIG. 13 is a handshake diagram showing a sequence of the control of thesender's timing, in which parts (a) to (d) correspond to the fourcombinations of a basis and a random number, respectively.

FIG. 14 is a flowchart showing a procedure of the control of thesender's timing, in a quantum cryptographic system according to a thirdembodiment of the present invention.

FIGS. 15A to 15D are graphs corresponding to the four combinations of abasis and a random number, respectively, each showing variations in theeffective photon counts and extinction ratio measured at the receiver.

FIGS. 16A to 16D are graphs corresponding to the four combinations of abasis and a random number, respectively, each showing variations in thephoton counts detected at the receiver.

FIG. 17A is a diagram schematically showing a data table of the ratiosbetween the photon counts of the photon detectors APD0 and APD1 and theamounts of the clock shift on the sender side, stored in the memory 270.

FIG. 17B is a diagram schematically showing a data table of the ratiosbetween the photon counts of the photon detectors APD0 and APD1 and theamounts of the clock shift on the receiver side, stored in the memory270.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 2 is a block diagram showing a schematic configuration of aweak-light power measurement apparatus according to a mode of thepresent invention. A photon detector 1 is an optical-to-electricalconversion device that can detect the presence or absence of theincidence of a single photon when bias voltage is being applied, and istypically an avalanche photodiode. The photon detector 1 is driven bybias voltage applied from a bias application circuit 2. The timing ofthe bias voltage application and the duration thereof are controlled bya timing control circuit 3. In other words, the photon detector 1 isoperated in a gated Geiger mode in which bias voltage is applied onlywhen an optical pulse is about to be detected, and is capable ofhigh-sensitivity reception.

The timing control circuit 3 can freely shift the phase of a clocksignal CLK in steps of 2π/n from 0 to 2π along the time axis, based ontiming shift control from an optical power measurement section 4. It isassumed here that the period of the clock signal CLK is substantiallycoincident with the period of incoming optical pulses, but that it isunknown which phase the arrivals of the optical pulses coincide with.Incidentally, as an example, an optical pulse has a pulse width of aboutone nanosecond, the pulse-shaped bias voltage applied to the photondetector 1 has a pulse width of about one to five nanoseconds, and thesepulses have a period T of about 16 nanoseconds.

The photon detector 1 can detect photon arrival as an optical pulse ifthe timing of the phase-shifted clock signal coincides with the timingof the arrival of the optical pulse. When photon arrival is detected bythe photon detector 1, it is counted by a photon counter 5. The photoncounter 5 stores the number of counted photons in a memory 6, under thecontrol of the optical power measurement section 4. However, the numberof counted photons actually includes the number of counted dark noises.

The optical power measurement section 4, as will be described later,sequentially shifts the phase of the clock signal CLK by 2π/n at a time,from 0 to 2π, whereby bias voltage is applied to the photon detector 1at the timing corresponding to each shifted clock phase. Each time ashift is made, the clock phase and the number of detected photons arestored in the memory 6. When the phase of the clock signal CLK isshifted up to 2π, the optical power measurement section 4 measures theoptical power of the train of optical pulses that have arrived, based onthe data stored in the memory 6. Assuming that a time intervalcorresponding to the period T of the clock signal CLK is referred to asa time slot, shifting the phase of the clock signal CLK from 0 up to 2πis equivalent to temporally moving the bias voltage application timingin the full range of the time slot.

Note that the optical power measurement section 4 can be implemented byexecuting a power measurement program stored in a program memory 7, on acomputer or program-controlled processor. Hereinafter, a weak-lightpower measurement method according to the present mode will be describedin detail.

FIG. 3 is a waveform diagram for describing the states of phase shiftsfor the bias application timing, in the weak-light power measurementmethod according to the present mode. FIG. 4 is a graph schematicallyshowing the photon count varying with the amount of the phase shift.

As shown in FIG. 3, first, the optical power measurement section 4 setsa timing shift θ, made in the clock signal CLK of the timing controlcircuit 3, at zero. Next, the optical power measurement section 4 causesthe timing control circuit 3 to shift the timing of the clock signal CLKby one step (2π/n). As a result, the timing of applying the pulse biasto the photon detector 1 is shifted by 2π/n. In accordance with thistiming, pulses of bias voltage are applied to the photon detector 1 fora certain period of time (actually, a period of time corresponding to aplurality of time slots). If a photon arrives, or a dark noise occurs,while this bias voltage is being applied, it is counted as photondetection by the photon counter 5. The number of counted photons isstored in the memory 6.

The optical power measurement section 4 similarly repeats the shiftingof the timing of the clock signal CLK by 2π/n, n times. Each time ashift is made, the number of photons counted by the photon counter 5 isstored in the memory 6, along with the amount of a phase shift at thattime if necessary. The amount of the clock shift, θ_(j), and the numberof the counted photons, c_(j), when j timing shifts have been made, canbe graphed as shown in FIG. 4.

Although in the varying count values shown in FIG. 4 there is anapparent peak around a certain amount of the phase shift, a peak doesnot always appear. When no photon arrives, only a dark count is made, inwhich case a peak as shown in FIG. 4 does not appear, and the countvalues are low at any phases. If a photon arrives, a peak as shown inFIG. 4 appears only at a phase corresponding to the photon arrivaltiming in question.

As shown in FIG. 4, assuming that P is the sum of the photon counts madewhen the clock timing has been shifted n times, P is represented by thefollowing equation:

$P = {\sum\limits_{i = 1}^{n}{c_{i}.}}$

This total photon count, P, corresponds to the diagonally hatched areain FIG. 4, surrounded by the vertical lines at θ=0 and θ=2π and thecurve showing the photon count c_(j). That is, this represents theaverage optical power. Accordingly, the optical power of very weak lightcan be measured with the photon detector, by counting the number ofphotons while the timing of applying bias to the photon detector 1 issequentially shifted from 0 to 2π as described above.

Next, embodiments will be described in which the above-describedweak-light power measurement method is actually applied to theinterference measurement in a quantum cryptographic system.

1. First Embodiment

FIG. 5 is a block diagram showing a configuration of atemperature-independent plug and play system according to a firstembodiment of the present invention. Here, the system configuration isillustrated as an example, in which, of two communication devices thatperform quantum communications, the sending side of the quantumcommunications is referred to as a sender 10, the receiving side thereofis referred to as a receiver 20, and the sender 10 and receiver 20 areoptically connected through an optical transmission line 30.

The basic configuration and operations of the plug and play systemaccording to the first embodiment are as described with reference toFIG. 1, except that a PBS loop is employed at the sender 10 in place ofa Faraday mirror.

A quantum block 100 at the sender 10 has a PBS loop 104, which includesa phase modulator 102 and a polarization beam splitter (PBS) 103.

The phase modulator 102 performs phase modulation on a train of passingoptical pulses, in accordance with a clock signal supplied from asynchronization block 110. The depth of a phase modulation is determinedby a phase control signal given from a communication controller 130.Here, there are four depths (0, π/2, π, 3π/2) corresponding to fourcombinations of a basis (+/×) and a random number (0/1). The phasecontrol signal is a voltage corresponding to any one of the modulationdepths. The phase control signal is applied to the phase modulator 102at the timing when an optical pulse is passing through the phasemodulator 102, whereby the optical pulse is phase-modulated.

The PBS loop 104 has a function similar to that of a Faraday mirror andoutputs incident light with its polarization state rotated by 90degrees. The PBS loop of the present embodiment will be described later.

Moreover, the sender 10 is provided with the synchronization block 110,a data communication section 120, and the communication controller 130.Under the control of the communication controller 130, thesynchronization block 110 exchanges clock signals with the receiver 20and supplies a clock signal CLK to the phase modulator 102. Thecommunication controller 130 exchanges control signals with the receiver20 through the data communication section 120 and controls the quantumblock 100 and synchronization block 110 in accordance with the controlsignals from the receiver 20.

The configuration of a quantum block 200 at the receiver 20 is basicallythe same as the configuration shown in FIG. 1. An optical pulse P,generated by a laser 201 in accordance with a reference clock signal, isled by an optical circulator 202 into an optical coupler 203, where theoptical pulse P is split into two parts. One of the two parts, anoptical pulse P1, goes along a short path 204 and is sent to apolarization beam splitter (PBS) 207. The other one, an optical pulseP2, is passed through a phase modulator 206, which is provided in a longpath 205, and then sent to the PBS 207. These optical pulses P1 and P2are combined at the PBS 207 and transmitted to the sender 10 as doublepulses, through a wavelength multiplexing/demultiplexing filter 50 andthe optical transmission line 30. Each of the double pulses returnedfrom the sender 10 is sent, by the PBS 207, into the other path that isdifferent from the path the optical pulse used when it was transmittedto the sender 10, and the optical pulses interfere with each other atthe optical coupler 203, which will be described later. The result ofthis interference is detected by a photon detector 208 (hereinafter,referred to as APD0), or a photon detector 209 (hereinafter, referred toas APD1). Incidentally, the short path 204 and long path 205 arepolarization-maintained fiber, and the optical circulator 202 andoptical coupler 203 are of polarization-maintained types.

The receiver 20 is provided with a synchronization block 210 thatsupplies the quantum block 200 with a clock signal CLK1 for phasemodulation and with a clock signal CLK2 for the operation of the photondetectors in the gated Geiger mode. The synchronization block 210exchanges synchronization clock signals with the synchronization block110 at the sender 10. Moreover, a communication controller 230 at thereceiver 20 exchanges control signals with the sender 10 through a datacommunication section 220 and controls the quantum block 200 andsynchronization block 210.

In addition to these blocks and sections, the receiver 20 in the systemaccording to the present embodiment is provided with a timing controller240 that optimizes the timing in the sender 10 and the timing in thereceiver 20 by controlling the communication controller 230, and with apower measurement section 250 for measuring optical power by using thephoton detectors APD0 and APD1. The optical power measurement section250 controls the timing controller 240, a photon counter 260 and amemory 270; has the photon counter 260 count the number of photonsdetected by the photon detectors APD0 and APD1 individually; and storesthe count values in the memory 270 as measurement data used to determinethe optimal timing and to measure the optical power. The timingcontroller 240 and optical power measurement section 250 can beimplemented by executing a program stored in a program memory 280, on acomputer or program-controlled processor.

Incidentally, a clock signal sent and received between thesynchronization blocks 110 and 210 and a control signal sent andreceived between the data communication sections 120 and 220 are signalseach having a wavelength different from that of the optical pulses sentand received between the quantum blocks 100 and 200. These signals arewavelength-multiplexed and -demultiplexed by the wavelengthmultiplexing/demultiplexing filters 40 and 50 and are transmitted overthe optical transmission line 30 by using wavelength divisionmultiplexing technology. In addition, the synchronization block 110provided to the sender 10 and the synchronization block 210 provided tothe receiver 20 each have a wavelength stabilized laser as a lightsource that sends out a clock signal. Accordingly, it is possible tosupply a stabilized clock signal to each of the quantum blocks 100 and200.

Next, a further detailed description will be given of the paths of thedouble pulses P1 and P2 after output to the optical transmission line 30from the quantum block 200 at the receiver 20, and the processing duringthe propagation of the double pulses P1 and P2 along the respectivepaths.

In the sender 10, each of the double pulses P1 and P2 that have arrivedthrough the optical transmission line 30 and wavelengthmultiplexing/demultiplexing filter 50 is further split at the PBS 103,resulting in four pulses (i.e., quartet pulses) including clockwisedouble pulses P1 _(cw) and P2 _(cw) and counterclockwise double pulsesP1 _(ccw) and P2 _(ccw). Each pair of the double pulses pass through thephase modulator 102 in the opposite direction to the other pair andenter a PBS port different from the port from which the pair wereoutput.

The phase modulator 102 phase-modulates the pulse P2 _(cw), which is thesecond one of the clockwise double pulses, with respect to the firstpulse P1 _(cw) and also gives a phase difference of π between thecounterclockwise double pulses and the clockwise double pulses, whichwill be described later. The phase modulator 102 needs such timingcontrol as to perform an arbitrary phase modulation on each of thequartet pulses as described above.

The quartet pulses thus phase-modulated as required are combined at thePBS 103, returning to the double pulses. As described above, since onlythe following one of the pulses has been phase-modulated based ontransmission information, the output double pulses are denoted by P1 andP2*^(a). At this point in time when the double pulses are output, thepolarization states of the double pulses have been rotated by 90 degreeswith respect to those when they were input. Consequently, an effectsimilar to a Faraday mirror can be obtained.

In the receiver 20, since the polarization states of the optical pulsesP1 and P2*^(a) received from the sender 10 have been rotated by 90degrees, the PBS 207 leads each of these received pulses into the otherpath that is different from the path the pulse used when it wastransmitted to the sender 10. Specifically, the received optical pulseP1 is led into the long path and phase-modulated based on a designatedbasis at the timing when it is passing through the phase modulator 206,and the phase-modulated optical pulse P1*^(b) arrives at the opticalcoupler 203. On the other hand, the optical pulse P2*^(a) passes alongthe short path, which is different from the path it used when it wastransmitted to the sender 10, and arrives at the same optical coupler203.

Thus, the optical pulse P2*^(a), phase-modulated on the sender side, andthe optical pulse P1*^(b), phase-modulated on the receiver side,interfere with each other, and the result of this interference isdetected by the photon detector APD0 or APD1. The photon detectors APD0and APD1 are driven in the gated Geiger mode in accordance with theclock signal CLK2 supplied from the synchronization block 210, and theirdetection signals are output to the communication controller 230 and thephoton counter 260. As will be described later, the timing controller240 accumulates in the memory 270 the detection signals detected by thephoton detectors APD0 and APD1 in a sequence of timing control, and usesthem to determine the optimal timing. In addition, the count value madeby the photon counter 260 is also stored in the memory 270 along withthe then amount of a phase shift.

1.1) Phase Modulation by PBS Loop

Hereinafter, the operation of the PBS loop will be described.

FIG. 6 is a schematic configuration diagram for describing the operationof the PBS loop at the sender. As described above, each of the incomingdouble pulses P1 and P2 is split at the PBS 103 into orthogonalpolarization components, resulting in the quartet pulses 301 to 304. Theoptical pulses 301 and 302 correspond to one polarization component ofthe optical pulse P1 and the other component perpendicular to it. Theoptical pulses 303 and 304 correspond to one polarization component ofthe optical pulse P2 and the other component perpendicular to it.

Two loop-side ports of the PBS 103 are respectively connected to twooptical ports of the phase modulator 102 by polarization-maintainedoptical fiber. However, the lengths of the optical paths between theseports are different from each other. It is assumed here that the lengthsof the optical paths are set so that the optical pulses 301 and 303enter the phase modulator 102 earlier than the optical pulses 302 and304 by a period of time T, respectively. This time difference T is setso as to be longer than the width of an optical pulse and shorter thanthe interval between the double pulses P1 and P2.

FIG. 7 is an explanatory diagram showing a time sequence of the opticalpulses propagating through the PBS loop. Since the optical pulses 301and 303 arrives at the phase modulator 102 earlier than the opticalpulses 302 and 304 by the period of time T, respectively, the opticalpulses pass through the phase modulator 102 at different times t1 to t6as shown in FIGS. 7(A) to 7(F). Therefore, the voltage to be applied tothe phase modulator 102 is varied in synchronization with the pulseintervals, whereby different phase differences can be given between theoptical pulses. Here, the phase differences to be given between theindividual pulses are set as shown in Table I.

TABLE I Phase of Phase of Phase of Phase of Optical Pulse Optical PulseOptical Pulse Optical Pulse Basis, RN 301 302 303 304 +, 0 0 π 0 π +, 10 π π 0 ×, 0 0 π   π/2 3 π/2 ×, 1 0 π 3 π/2   π/2

As shown in Table I, when the basis is “+” and the random number valueis “0”, a phase difference of 0 is given between the optical pulses 301and 303. When the basis is “+” and the random number value is “1”, aphase difference of π is given between the optical pulses 301 and 303.When the basis is “×” and the random number value is “0”, a phasedifference of π/2 is given between the optical pulses 301 and 303. Whenthe basis is “×” and the random number value is “1”, a phase differenceof 3π/2 is given between the optical pulses 301 and 303. Moreover, aphase difference of the same size as that between the optical pulses 301and 303 is given between the optical pulses 302 and 304. At the sametime, a phase difference of π is given between the optical pulses 301and 302, and also between the optical pulses 303 and 304.

As described above, in a quantum key distribution system, an arbitraryphase modulation needs to be performed on each of the double pulses orquartet pulses. That is, it is necessary to apply a voltage for giving arequired modulation to each of the phase modulators 102 and 206, whichcontrol the phase by using voltage, at the timing when each pulse ispassing through the phase modulator. If the phase modulator is notdriven at the right timing, a false pulse will be modulated. Therefore,it is necessary to control the timings of the clock signals for drivingthe phase modulators 102 and 206, and to check whether the timings areright.

1.2) Measurement of Extinction Ratio

FIG. 8 is a flowchart showing a search for the timing in the sender 10,including a procedure of measuring an extinction ratio at the receiver20, in the system according to the first embodiment of the presentinvention. To check whether or not the timing of the clock signal CLKfor driving the phase modulator 102 at the sender 10 is right, theextinction ratio needs to be measured at the receiver 20. Here, theextinction ratio is the ratio between the optical powers output to thephoton detectors APD0 and APD1.

However, as mentioned already, a photon detector APD can only determinethe presence or absence of the arrival of a photon but cannot directlymeasure the optical power, which is the time average of photondetections. Therefore, according to the present embodiment, the timingof the clock signal CLK2 for driving the photon detectors APD issequentially shifted, whereby the optical powers are obtained indirectlyfrom the results of photon detection achieved by the photon detectorseach time a shift is made.

Referring to FIG. 8, first, the timing controller 240 controls thecommunication controller 230 so that one of the four combinations of abasis and a random number is selected, that the selected basis is set onthe phase modulator 206 at the receiver 20, and that the selectedcombination of a basis and a random number value is notified fordesignation to the communication controller 130 at the sender 10 (S401).Upon this designation, the communication controller 130 outputs phasecontrol signals to the phase modulator 102 and thereby sets the phase atmodulation depths corresponding to the selected basis and random numbervalue.

Subsequently, the timing controller 240 instructs the communicationcontroller 130 at the sender 10 to reset a timing shift made for thetiming of applying voltage to the phase modulator 102 at the sender 10(S402). At this instruction, the synchronization block 110 resets theamount of the shift in the clock signal CLK to an initial value of zero.

Upon the initialization of the timing shift, the timing controller 240instructs the communication controller 130 to make a timing shift,whereby the synchronization block 110, using a predetermined integer N,shifts the timing of applying voltage to the phase modulator 102 by2π/N. In accordance with this timing, voltages corresponding to the setphase modulations are applied (S403). Thus, each of the passing quartetoptical pulses is modulated as described above and then sent back to thereceiver 20 in the form of the double pulses.

In the receiver 20, the phase modulator 206 modulates the receiveddouble pulses, based on the basis designated as described above. Thedouble pulses are made to interfere with each other at the opticalcoupler 203, and photon detection is performed by the photon detectorsAPD0 and APD1. At this time, it is necessary that bias voltage be raisedonly at the timing when a photon is coming in, for the photon detectorsAPD0 and APD1 to receive the photon. That is, it is necessary to drivethe photon detectors APD with a clock signal the timing of which iscoincident with the timing of the arrival of the photon. However, atthis point in time, it is unknown at which timing in the full phaserange (2π) of the clock signal, the photon comes in.

Therefore, the timing controller 240 instructs the communicationcontroller 230 to reset a timing shift made for the timing of applyingbias to the photon detectors APD0 and APD1 at the receiver 20. At thisinstruction, the synchronization block 210 resets the amount of theshift in the clock signal CLK2 to an initial value of zero (S404).

Next, the timing controller 240 instructs to shift the timing of theclock signal CLK2 to be output from the synchronization block 210, byone step. Using a predetermined integer n, the synchronization block 210shifts the timing of applying bias to the photon detectors APD0 and APD1by 2π/n (S405). With this shift, bias voltage is applied to the photondetectors APD0 and APD1 at the timing shifted by 2π/n, and then photondetection is performed. Each time a photon is detected by any of thephoton detectors, the number of photons detected by each photon detectoris counted by the photon counter 260. The operation of counting thenumber of photons is repeated n times while the phase for the biasapplication timing is sequentially and continuously shifted by one step(2π/n) each time (S406).

When the amount of the shift reaches 2π in this manner, the number ofphotons counted until this point by the photon counter 260 for each ofthe photon detectors is stored in the memory 270, associated with thecurrently designated random number and basis and with the amount of theshift for the phase modulation timing, φ_(i) (i=1 to N), currently madeat the sender 10 (S407). Here, as mentioned with reference to FIG. 4,the number of photons recorded in the memory 270 corresponds to the areaof the region between t=0 and t=2 π, which, in other words, means theoptical power.

The timing controller 240 repeats the steps S403 to S407 N times (S408),in which each time the timing of applying voltage to the phase modulator102 is shifted by 2π/N, the timing of applying bias to the photondetectors APD0 and APD1 is sequentially shifted from 0 to 2π and thenumber of detected photons is counted. When these steps S403 to S407have been repeated until the photon counts are measured for all thetimings of applying voltage to the phase modulator 102 (YES at S408),the next basis and random number value are designated (S401), and thenthe above-described steps S402 to S408 are repeated.

The timing controller 240 performs the steps S401 to S408 for every oneof the four combinations of a basis and a random number (S409). However,if an optimal point, which will be described later, can be found, it isnot necessary to perform these steps for all the four combinations. Whenmeasurement is finished for the required combinations of a basis and arandom number (YES at S409), the timing controller 240 determines theoptimal timing in the sender 10, based on the respective photon countsof the photon detectors APD0 and APD1, recorded in the memory 270. Thetiming controller 240 notifies the communication controller 130 of thisoptimal timing, which is then set on the synchronization block 110(S410).

1.3) Search for Clock Timing in Sender 10

FIG. 9 is a handshake diagram showing a timing control sequence of thesender, in which parts (a) to (d) correspond to the four combinations ofa basis and a random number, respectively. FIGS. 10A to 10D are graphscorresponding to the four combinations of a basis and a random number,respectively, each showing variations in the effective photon counts andextinction ratio measured at the receiver.

a) Basis +, Random Number 0 (0 Modulation)

First, the timing controller 240 at the receiver 20 sets the receptionbasis of the phase modulator 206 at “+”, and further instructs thecommunication controller 130 at the sender 10 to set the phase modulator102 at modulation depths corresponding to the basis “+” and the randomnumber “0”. As a result, as shown in Table I mentioned before, thephases for phase modulation to be given to the individual quartetoptical pulses are “0-π-0-π”, in the order in which the quartet pulsespass through the phase modulator 102.

Since the phase modulator 102 at the sender 10 is driven in accordancewith the clock signal supplied from the synchronization block 110, thetiming at which the phase modulator 102 phase-modulates the opticalpulses depends on the timing of supplying the clock signal. Inaccordance with instructions from the receiver 20, the synchronizationblock 110 can shift the timing of the clock signal from 0 to 2π by anarbitrary number of steps.

Subsequently, the timing controller 240 instructs to clear to zero theamount of the shift in the clock signal CLK of the synchronization block110 at the sender 10. Then, the undermentioned steps S1 to S5 arerepeated N times while the amount of the clock shift is increased by2π/N each time, until it reaches 2π.

Step S1: The timing controller 240 at the receiver 20 instructs thecommunication controller 130 at the sender 10 to shift the clock signalCLK of the synchronization block 110 by one step, and also instructs thecommunication controller 230 at the receiver 20 to clear to zero theamount of the shift in the clock signal CLK2 of the synchronizationblock 210.

Step S2: The communication controller 130 at the sender 10 has thesynchronization-block 110 shift the clock signal CLK by one step. Withthis shift, the timing of driving the phase modulator 102 at the sender10 is shifted by one step.

Step S3: With this one-step shift made at the sender 10, the opticalpowers observed by the photon detectors APD0 and APD1 at the receiver 20are each changed.

Step S4: The communication controller 230 at the receiver 20 has thesynchronization block 210 sequentially and continuously shift the clocksignal CLK2 step by step from 0 to 2π. With these shifts, the timing ofdriving the photon detectors APD0 and APD1 is sequentially andcontinuously changed from 0 to 2π. During this operation, the photoncounter 260 is incremented each time a photon is detected. Accordingly,when the clock signal CLK2 has been shifted from 0 to 2π, the totalphoton count is stored in the photon counter 260. The photon count isstored without corresponding to the amount of the phase shift. Thisprovides the advantage of high-speed processing and easy installation.

Step S5: The respective results of the photon detection by the photondetectors APD0 and APD1, counted by the photon counter 260, are storedin the memory 270. In this event, the photon counter 260 only countsphotons that are detected while the clock signal CLK2 of thesynchronization block 210 is being sequentially shifted in the step S4,and stores the detected photons in the memory 270 as an effective photoncount. In other words, the effective photon count is a real count valueexcluding the number of photons counted by the photon counter 260 beforethe shifting of the phase of the clock signal CLK2 is started and afterit is finished.

FIG. 10A shows the effective photon counts varying with the amount ofthe timing shift φ_(i) made at the sender 10, thus stored in the memory270. In FIG. 10A, the horizontal axis represents the amount of the clockshift φ_(i) made at the sender 10, and the vertical axis represents theeffective photon count of APD0 (solid line) and APD1 (dashed line).

From this graph, the extinction ratio (dotted line) can be obtained asthe ratio of the effective photon count of the photon detector APD0 tothe effective photon count of the photon detector APD1 (P₀/P₁). Thereason for P₀/P₁ is that when the clock phase at the sender 10 is right,an optical pulse is detected by the photon detector APD0 but hardly bythe photon detector APD1.

b) Basis +, Random Number 1 (π Modulation)

The timing controller 240 at the receiver 20 instructs the communicationcontroller 130 at the sender 10 to set the phase modulator 102 atmodulation depths corresponding to the basis “+” and the random number“1”, while leaving the basis in the receiver 20 at “+”. As a result, asshown in Table I mentioned above, the phases for phase modulation to begiven to the individual quartet optical pulses are “0-π-π-0”, in theorder in which the quartet pulses pass through the phase modulator 102.

Subsequently, the timing controller 240 instructs to clear to zero theamount of the shift in the clock signal CLK of the synchronization block110 at the sender 10. Then, the above-described steps S1 to S5 arerepeated N times while the amount of the clock shift at the sender 10 isincreased by 2π/N each time, until it reaches 2π. With these shifts, theoptical powers observed by the photon detectors APD0 and APD1 at thereceiver 20 are each changed. While the clock signal CLK2 at thereceiver 20 is sequentially and continuously shifted, the effectivephoton counts are stored in the memory 270.

FIG. 10B shows the effective photon counts varying with the amount ofthe timing shift φ_(i) made at the sender 10, thus stored in the memory270. In FIG. 10B, the horizontal axis represents the amount of the clockshift φ_(i) made at the sender 10, and the vertical axis represents theeffective photon count of APD0 (solid line) and APD1 (dashed line).

From this graph, the extinction ratio (dotted line) can be obtained asthe ratio of the effective photon count of the photon detector APD1 tothe effective photon count of the photon detector APD0 (P₁/P₀). Thereason for P₁/P₀ is that when the clock phase at the sender 10 is right,an optical pulse is detected by the photon detector APD1 but hardly bythe photon detector APD0.

c) Basis ×, Random Number 0 (π/2 Modulation)

The timing controller 240 at the receiver 20 sets the reception basis ofthe phase modulator 206 at “×”, and further instructs the communicationcontroller 130 at the sender 10 to set the phase modulator 102 atmodulation depths corresponding to the basis “×” and the random number“0”. As a result, as shown in Table 1 mentioned above, the phases forphase modulation to be given to the individual quartet optical pulsesare “0-π-π/2-π/2”, in the order in which the quartet pulses pass throughthe phase modulator 102.

Subsequently, the timing controller 240 instructs to clear to zero theamount of the shift in the clock signal CLK of the synchronization block110 at the sender 10. Then, the above-described steps S1 to S5 arerepeated while the amount of the clock shift made at the sender 10 isincreased by 2π/N each time, until it reaches 2π. With these shifts, theoptical powers observed by the photon detectors APD0 and APD1 at thereceiver 20 are each changed. While the clock signal CLK2 at thereceiver 20 is sequentially and continuously shifted, the effectivephoton counts are stored in the memory 270.

FIG. 10C shows the effective photon counts varying with the amount ofthe timing shift φ_(i) made at the sender 10, thus stored in the memory270. In FIG. 10C, the horizontal axis represents the amount of the clockshift φ_(i) made at the sender 10, and the vertical axis represents theeffective photon count of APD0 (solid line) and APD1 (dashed line).

From this graph, the extinction ratio (dotted line) can be obtained asthe ratio of the effective photon count of the photon detector APD0 tothe effective photon count of the photon detector APD0 (P₀/P₁). Thereason for P₀/P₁ is that when the clock phase at the sender 10 is right,an optical pulse is detected by the photon detector APD0 but hardly bythe photon detector APD1.

d) Basis ×, Random Number 1 (3π/2 Modulation)

The timing controller 240 at the receiver 20 instructs the communicationcontroller 130 at the sender 10 to set the phase modulator 102 atmodulation depths corresponding to the basis “×” and the random number“1”, while leaving the basis in the receiver 20 at “×”. As a result, asshown in Table 1 mentioned above, the phases for phase modulation to begiven to the individual quartet optical pulses are “0-π-3π/2-π/2”, inthe order in which the quartet pulses pass through the phase modulator102.

Subsequently, the timing controller 240 instructs to clear to zero theamount of the shift in the clock signal CLK of the synchronization block110 at the sender 10. Then, the above-described steps S1 to S5 arerepeated N times while the amount of the clock shift made at the sender10 is increased by 2π/N each time, until it reaches 2π. With theseshifts, the optical powers observed by the photon detectors APD0 andAPD1 at the receiver 20 are each changed. While the clock signal CLK2 atthe receiver 20 is sequentially and continuously shifted, the effectivephoton counts are stored in the memory 270.

FIG. 10D shows the effective photon counts varying with the amount ofthe timing shift φ_(i) made at the sender 10, thus stored in the memory270. In FIG. 10D, the horizontal axis represents the amount of the clockshift φ_(i) made at the sender 10, and the vertical axis represents theeffective photon count of APD0 (solid line) and APD1 (dashed line).

From this graph, the extinction ratio (dotted line) can be obtained asthe ratio of the effective photon count of the photon detector APD1 tothe effective photon count of the photon detector APD0 (P₁/P₀). Thereason for P₁/P₀ is that when the clock phase at the sender 10 is right,an optical pulse is detected by the photon detector APD1 but hardly bythe photon detector APD0.

1.4) Determination of Optimal Timing in Sender

Referring to FIGS. 10A to 10D, the ratio between the optical powersdetected by APD0 and APD1, that is, the extinction ratio is indicated bya dotted line. As described above, the extinction ratio is representedby P₀/P₁ when the random number “0” is sent, and is represented by P₁/P₀when the random number “1” is sent. The effective photon counts outputto the photon detectors APD0 and APD1 and the amount of the clock shiftφ_(i) then made at the sender 10, are all stored in the memory 270 atthe receiver 20. Based on this data, the timing controller 240determines the optimal timing of the clock signal CLK at the sender 10.

FIG. 11 is a diagram schematically showing a data table of the ratiosbetween the effective photon counts of the photon detectors APD0 andAPD1 and the amounts of the clock shift, stored in the memory 270. Thatis, the observation data corresponding to the respective fourcombinations of a basis and a random number shown in FIGS. 10A to 10D isstored in the form of a table as shown in FIG. 11. Using this datatable, the optimal timing is determined through the following procedure.

(1) The extinction ratio is calculated for each of the four types ofmodulation: (Ai, Bi, Ci, Di).

(2) The product of the four extinction ratios is calculated:(Ei=Ai*Bi*Ci*Di).

(3) A phase that makes maximum Ei is selected: (φ_(i) (max [E1, E2, . .. , EN])).

The amount of the shift φ_(i) determined in such a manner is a valueφ_(suit) indicated by the “OPTIMAL” line in FIGS. 10A to 10D. The clocksignal CLK shifted by this amount provides the optimal timingsynchronizing with the optical pulses. However, as mentioned already, ifit is possible to obtain the optimal line, there is no need to use allthe observation data corresponding to the four combinations shown inFIGS. 10A to 10D.

1.5) Advantages

As described above, according to the present embodiment, first, thetiming for the phase modulator 102 at the sender 10 is shifted on astep-by-step basis in accordance with the control from the receiver 20.Each time a shift is made, the timing of raising bias to be applied tothe photon detectors at the receiver 20 is sequentially and continuouslyshifted from 0 to 2π, and the results of photon detection are stored inthe memory 270. In the results of the photon detection, only the photonsthat are detected while the timing of raising bias is being sequentiallyshifted are processed as the effective photon counts. Based on theseeffective photon counts, the optimal timing of the phase modulation atthe sender 10 is determined. Accordingly, it is possible for thereceiver side to check, by using the photon detectors APD, whether ornot the timing of the phase modulation at the sender 10 is right. Thus,stable phase modulation can be performed in the sender 10. In the caseof applying the present embodiment to a quantum key distribution system,it is possible to achieve high-speed, stable key generation.

2. Second Embodiment

FIG. 12 is a flowchart showing a procedure of the control of thesender's timing, in a quantum cryptographic system according to a secondembodiment of the present invention. The block configuration of thequantum cryptographic system according to the second embodiment issimilar to that of the first embodiment as shown in FIG. 5. The opticalpulses to be sent and received behave as in the first embodiment, asdescribed based on FIGS. 6 and 7. Therefore, a description of the partsoverlapping with the first embodiment will be omitted. With reference toFIGS. 5 and 12, operations of determining the extinction ratio, ofsearching for the sender's clock timing, and of determining the optimaltiming will be described in detail.

2.1) Measurement of Extinction Ratio

The timing controller 240 controls the communication controller 230 sothat one of the four combinations of a basis and a random number isselected, that the selected basis is set on the phase modulator 206 atthe receiver 20, and that the selected combination of a basis and arandom number value is notified for designation to the communicationcontroller 130 at the sender 10 (S501). With this designation, thecommunication controller 130 outputs phase control signals to the phasemodulator 102, thereby setting the phase at modulation depthscorresponding to the selected basis and random number value.

Subsequently, the timing controller 240 instructs the communicationcontroller 130 at the sender 10 to reset a timing shift made for thetiming of applying voltage to the phase modulator 102 at the sender 10(S502). At this instruction, the synchronization block 110 resets theamount of the shift in the clock signal CLK to an initial value of zero.

Upon the initialization of the timing shift, the timing controller 240instructs the communication controller 130 to make a timing shift. Atthis instruction, the synchronization block 110, using a predeterminedinteger N, shifts the timing of applying voltage to the phase modulator102 by 2π/N, and voltages corresponding to the set phase modulations areapplied in accordance with this timing (S503). Thus, the passing quartetoptical pulses are individually modulated as described above and thenreturned to the receiver 20 in the form of the double pulses.

In the receiver 20, the received double pulses are modulated by thephase modulator 206 with the basis designated as described above andmade to interfere with each other at the optical coupler 203, and thenphoton detection is performed by the photon detectors APD0 and APD1. Atthis time, it is necessary that bias voltage be raised only at thetiming when a photon is coming in, for the photon detectors APD0 andAPD1 to receive the photon. That is, it is necessary to drive the photondetectors APD with a clock signal the timing of which is coincident withthe timing of the arrival of the photon. However, at this point in time,it is unknown at which timing in the full phase range (2π) of the clocksignal, the photon comes in.

Therefore, the timing controller 240 instructs to reset a timing shiftmade for the timing of applying bias to the photon detectors APD0 andAPD1 at the receiver 20 (S504). With this instruction, thesynchronization block 210 resets the amount of the shift in the clocksignal CLK2 to an initial value of zero.

Next, the timing controller 240 instructs to shift the timing ofapplying bias to the photon detectors APD0 and APD1 by 2π/n (S505). Aphoton detected by the photon detector APD0 or APD1 during this biasapplication is counted by the photon counter 260. The count is stored inthe memory 270, associated with the currently designated random numberand basis, the amount of the timing shift φ_(i) (i=1 to N) currently setat the sender 10, and the current amount of the shift θ_(j) (j=1 to n)in the clock signal CLK2 (S506).

Leaving the timing of applying voltage to the phase modulator 102 at thesender 10 unchanged, the timing controller 240 repeats theabove-described steps S505 and S506 while shifting the timing ofapplying bias to the photon detectors APD0 and APD1 by 2π/n each time,until the photon counts are recorded in the memory 270 for all the biasapplication timings (S507).

When the timing shift at the receiver 20 is finished (YES at S507), thetiming controller 240 instructs to shift the timing of applying voltageto the phase modulator 102 at the sender 10 by 2π/N (S508 and S503) andagain repeats the steps S505 and S506. The steps S503 to S507 arerepeated until the photon counts are measured for all the voltageapplication timings, whereby photon detection and photon counting areperformed for the currently selected basis and random number value(S508).

The timing controller 240 performs the above-described steps S501 toS508 for every one of the four combinations of a basis and a randomnumber (S509). When measurement is finished for all the fourcombinations of a basis and a random number (YES at S509), the timingcontroller 240 determines the optimal timing in the sender 10, based onthe photon counts of the photon detectors APD0 and APD1, recorded in thememory 270, and notifies the optimal timing to the communicationcontroller 130 at the sender 10 to set it on the synchronization block110 (S510).

2.2) Search for Clock Timing in Sender

FIG. 13 is a handshake diagram showing a sequence of the control of thesender's timing, in which parts (a) to (d) correspond to the fourcombinations of a basis and a random number, respectively.

a) Basis +, Random Number 0 (0 Modulation)

First, the timing controller 240 at the receiver 20 sets the receptionbasis of the phase modulator 206 at “+”, and further instructs thecommunication controller 130 at the sender 10 to set the phase modulator102 at modulation depths corresponding to the basis “+” and the randomnumber “0”. As a result, as shown in Table I mentioned above, the phasesfor phase modulation to be given to the individual quartet opticalpulses are “0-π-0-π”, in the order in which the quartet pulses passthrough the phase modulator 102.

Since the phase modulator 102 at the sender 10 is driven in accordancewith the clock signal CLK supplied from the synchronization block 110,the timing at which the phase modulator 102 phase-modulates the opticalpulses depends on the timing of supplying the clock signal CLK. Inaccordance with instructions from the receiver 20, the synchronizationblock 110 can shift the timing of the clock signal CLK from 0 to 2π byan arbitrary number of steps.

Subsequently, the timing controller 240 instructs to clear to zero theamount of the shift in the clock signal CLK of the synchronization block110 at the sender 10. Then, the undermentioned steps S1 to S5 arerepeated N times while the amount of the clock shift is increased by2π/N each time, until it reaches 2π.

Step S1: The timing controller 240 at the receiver 20 instructs thecommunication controller 130 at the sender 10 to shift the clock signalCLK of the synchronization block 110 by one step, and also instructs thecommunication controller 230 in the receiver 20 to clear to zero theamount of the shift in the clock signal CLK2 of the synchronizationblock 210.

Step S2: The communication controller 130 at the sender 10 has thesynchronization block 110 shift the clock signal CLK by one step. Withthis shift, the timing of driving the phase modulator 102 at the sender10 is shifted by one step.

Step S3: With the one-step shift at the sender 10, the optical powersobserved by the photon detectors APD0 and APD1 at the receiver 20 areeach changed.

Step S4: The communication controller 230 at the receiver 20 has thesynchronization block 210 shift the clock signal CLK2 by one step. Theamount of a clock shift per step is assumed to be 2π/n.

Step S5: When a photon is detected by the photon detector APD0 or APD1,this detection is counted by the photon counter 260, and the count valueis stored in the memory 270. Thereafter, the steps S4 and S5 arerepeated n times until the amount of the shift in the clock signal CLK2becomes 2π in the step S4.

Accordingly, each time the clock signal CLK at the sender 10 is shiftedby one step (2π/N), the clock signal CLK2 at the receiver 20 issequentially shifted step by step from 0 to 2π, wherein each time theclock signal CLK2 is shifted by one step, the count value made by thephoton counter 260 is stored in the memory 270, associated with the thenamount of the phase shift θ_(j).

b) Basis +, Random Number 1 (× Modulation)

The timing controller 240 at the receiver 20 instructs the communicationcontroller 130 at the sender 10 to set the phase modulator 102 atmodulation depths corresponding to the basis “+” and the random number“1”, while leaving the basis in the receiver 20 at “+”. As a result, asshown in Table I mentioned above, the phases for phase modulation to begiven to the individual quartet optical pulses are “0-π-π-0”, in theorder in which the quartet pulses pass through the phase modulator 102.

Subsequently, the timing controller 240 instructs to clear to zero theamount of the shift in the clock signal CLK of the synchronization block110 at the sender 10. Then, the above-described steps S1 to S5 arerepeated N time while the amount of the clock shift at the sender 10 isincreased by 2 π/N each time, until it reaches 2π. Accordingly, eachtime the clock signal CLK at the sender 10 is shifted by one step(2π/N), the clock signal CLK2 at the receiver 20 is sequentially shiftedstep by step from 0 to 2π, wherein each time the clock signal CLK2 isshifted by one step, the count value made by the photon counter 260 isstored in the memory 270, associated with the then amount of the phaseshift θ_(j).

c) Basis ×, Random Number 0 (π/2 Modulation)

The timing controller 240 at the receiver 20 sets the reception basis ofthe phase modulator 206 at “×”, and further instructs the communicationcontroller 130 at the sender 10 to set the phase modulator 102 atmodulation depths corresponding to the basis “×” and the random number“0”. As a result, as shown in Table I mentioned above, the phases forphase modulation to be given to the individual quartet optical pulsesare “0-π-π/2-3π/2”, in the order in which the quartet pulses passthrough the phase modulator 102.

Subsequently, the timing controller 240 instructs to clear to zero theamount of the shift in the clock signal CLK of the synchronization block110 at the sender 10. Then, the above-described steps S1 to S5 arerepeated N times while the amount of the clock shift is increased by2π/N each time, until it reaches 2π. Accordingly, each time the clocksignal CLK at the sender 10 is shifted by one step (2π/N), the clocksignal CLK2 at the receiver 20 is sequentially shifted step by step from0 to 2π, wherein each time the clock signal CLK2 is shifted by one step,the count value made by the photon counter 260 is stored in the memory270, associated with the then amount of the phase shift θ_(j).

d) Basis ×, Random Number 1 (3π/2 Modulation)

The timing controller 240 at the receiver 20 instructs the communicationcontroller 130 at the sender 10 to set the phase modulator 102 atmodulation depths corresponding to the basis “×” and the random number“1”, while leaving the basis in the receiver 20 at “×”. As a result, asshown in Table I mentioned above, the phases for phase modulation to begiven to the individual quartet optical pulses are “0-π-3π/2-π/2”, inthe order in which the quartet pulses pass through the phase modulator102.

Subsequently, the timing controller 240 instructs to clear to zero theamount of the shift in the clock signal CLK of the synchronization block110 at the sender 10. Then, the above-described steps S1 to S5 arerepeated N time while the amount of the clock shift at the sender 10 isincreased by 2 π/N each time, until it reaches 2π. Accordingly, eachtime the clock signal CLK at the sender 10 is shifted by one step(2π/N), the clock signal CLK2 at the receiver 20 is sequentially shiftedstep by step from 0 to 2π, wherein each time the clock signal CLK2 isshifted by one step, the count value made by the photon counter 260 isstored in the memory 270, associated with the then amount of the phaseshift θ_(j).

2.3) Determination of Optimal Timing in Sender

First, the ratio between the optical powers observed by the photondetectors APD0 and APD1, that is, the extinction ratio is obtained. Todo so, it is necessary to obtain the optical powers output to the photondetectors APD0 and APD1 when the amount of the timing shift at thesender 10 is φ_(i). When the amount of the timing shift at the sender 10is φ_(i), the bias application timing at the receiver 20 is shifted ntimes, by 2π/n each time. Assuming that c₀(i, j) and c₁(i, j) are thephoton counts of the photon detectors APD0 and APD1, respectively, madewhen the j-th shifting is performed, then the optical powers P₀(i) andP₁(i) observed by APD0 and APD1, respectively, when the amount of thetiming shift at the sender 10 is φ_(i), can be represented by thefollowing equations, respectively:

$\begin{matrix}{{P_{0}(i)} = {\sum\limits_{j = 1}^{n}{c_{0}( {i,j} )}}} & (1) \\{{P_{1}(i)} = {\sum\limits_{j = 1}^{n}{c_{1}( {i,j} )}}} & (2)\end{matrix}$

The optical powers thus obtained vary with the amount of the timingshift φ_(i) at the sender 10 as shown in FIG. 10A. In FIGS. 10A to 10D,the horizontal axes represent the amount of the clock shift φ_(i) at thesender, and the vertical axes represent the optical power observed byAPD0 (solid line) and by APD1 (dashed line). From these graphs, asdescribed above, the ratio between the optical powers observed by thephoton detectors APD0 and APD1, that is, the extinction ratio can beobtained (dotted line).

The extinction ratio is expressed as P₀/P₁ when the random number “0” issent, and is expressed as P₁/P₀ when the random umber “1” is sent. Theoptical powers output to the photon detectors APD0 and APD1 and theamount of the clock shift φ_(i) then made at the sender 10 are allstored in the memory 270 at the receiver 20. Based on this data, theoptimal timing of the clock signal CLK at the sender 10 is determined.The determination method is as described with reference to FIG. 11.

2.4) Advantages

As described above, according to the second embodiment of the presentinvention, each time the clock signal CLK at the sender 10 is shifted byone step (2π/N), the clock signal CLK2 at the receiver 20 issequentially shifted step by step from 0 to 2π. Therefore, the opticalpowers can be measured as in the first embodiment.

Moreover, according to the second embodiment, each time the clock signalCLK2 is shifted by one step, the count value made by the photon counter260 is stored in the memory 270, associated with the then amount of thephase shift θ_(j). Accordingly, it is possible to record how the photoncounts vary while the clock signal CLK2 is shifted from 0 to 2π. Forexample, it is possible to see that the photon counts vary as shown inFIG. 4.

3. Third Embodiment

As described above, according to the second embodiment, each time theclock signal CLK2 is shifted by one step, the count value made by thephoton counter 260 and the then amount of the phase shift are stored inthe memory 270, associated with each other. According to a thirdembodiment, by utilizing this data stored in the memory 270, not onlythe extinction ratio can be measured, but also the optimal timing can bedetermined for each of the sender and the receiver. Hereinafter, thethird embodiment will be described in detail.

FIG. 14 is a flowchart showing a procedure of the control of thesender's timing, in a quantum cryptographic system according to thethird embodiment of the present invention. The block configuration ofthe quantum cryptographic system according to the third embodiment issimilar to that of the first embodiment as shown in FIG. 5. The opticalpulses to be sent and received behave as in the first embodiment, asdescribed based on FIGS. 6 and 7.

Moreover, sender's timing search operations in the third embodiment aresimilar to the steps S501 to S509 described with reference to FIG. 12.Therefore, these parts are denoted by the same reference numerals andsymbols as in FIG. 12, and a description thereof will be omitted.Hereinafter, the determination of the optimal timing in the sender(S510) and the determination of the optimal timing in the receiver(S511) will be described. Note that the control of the timing in thesender 10 is all performed in accordance with instructions from thetiming controller 240 at the receiver 20.

3.1) Determination of Optimal Timing in Sender

FIGS. 15A to 15D are graphs corresponding to the four combinations of abase and a random number, respectively, each showing variations in theeffective photon counts and extinction ratio measured at the receiver.The horizontal axes represent the amount of a timing shift φ_(i) (i=1 toN) at the sender 10, and the vertical axes represent the optical power(photon count) observed by the photon detectors APD0 and APD1. Here, theoptical power observed by the photon detector APD0 is shown by a solidline, and the optical power observed by the photon detector APD1 isshown by a dashed line.

As described above, when the amount of the timing shift at the sender 10is φ_(i), the bias application timing at the receiver 20 is shifted ntimes, by 2π/n each time (S505 to S507). Assuming that c₀(i, j) andc₁(i, j) are the photon counts of the photon detectors APD0 and APD1,respectively, made when the j-th shifting is performed, then the opticalpowers P₀(i) and P₁(i) observed by APD0 and APD1, respectively, when theamount of the timing shift at the sender 10 is φ_(i), can be representedby the above-mentioned equations (1) and (2), respectively.

The optical powers thus obtained vary with the amount of the timingshift φ_(i) at the sender 10 as shown in FIG. 15A (same as FIG. 10A).From this graph, as described above, the ratio between the opticalpowers observed by the photon detectors APD0 and APD1, that is, theextinction ratio can be obtained (dotted line). As for FIGS. 15B to 15D,the description given with FIGS. 10B to 10D applies, respectively.

Moreover, the optical powers output to the photon detectors APD0 andAPD1 and the amount of the clock shift φ_(i) then made at the sender 10are all stored in the memory 270 at the receiver 20. Based on this data(see FIG. 17A) on the amount of the phase shift and the then opticalpowers (photon counts), the optimal timing of the clock signal CLK atthe sender 10 can be determined. The determination method is asdescribed with reference to FIG. 11.

3.2) Determination of Optimal Timing in Receiver

Once the optimal timing, φ_(suit), of the clock signal CLK at the sender10 is determined as described above (S510), the optimal timing in thereceiver 20 is subsequently determined by using the measurement datastored in the memory 270 (S511).

FIGS. 16A to 16D are graphs corresponding to the four combinations of abase and a random number, respectively, each showing variations in thephoton counts detected at the receiver. FIG. 16A shows the observationvalues varying with the amount of the timing shift θ_(j) (j=1 to n) atthe receiver 20, stored in the memory 270, for the combination of thebasis “+” and the random number “0”. In FIGS. 16A to 16D, the horizontalaxes represent the amount of the timing shift θ_(j) at the receiver 20,and the vertical axes represent the result of photon detection observedby APD0 (solid line) and by APD1 (dashed line).

Referring to FIG. 16A, when the clock phase is right, a photon isdetected by APD0 because the random number value sent from the sender 10is “0”. When the clock phase deviates, no photon is detected. Similarly,FIGS. 16B to 16D show observation values varying with the amount of thetiming shift θ_(j), in the case of the basis “+” and the random number“1”, in the case of the basis “×” and the random number “0”, and in thecase of the basis “×” and the random number “1”, respectively.

In FIGS. 16A to 16D, the ratio between the photon counts of APD0 andAPD1, that is, the photon detection ratio is shown by a dotted line. Inthe case where φ=φ_(suit) (φ is the timing of the clock signal CLK atthe sender 10), since light should be output to APD0 when the randomnumber “0” is sent, the ratio of the observation value obtained by APD0to the observation value obtained by APD1, c₀ (i_(suit), j)/c₁(i_(suit), j), is represented as photon detection. Moreover, when therandom number “1” is sent, since light should be output to APD1, theratio of the observation value obtained by APD1 to the observation valueobtained by APD0, c₁ (i_(suit), j)/c₀ (i_(suit), j), is represented asphoton detection.

FIG. 17A is a diagram schematically showing a data table of the ratiosbetween the photon counts of the photon detectors APD0 and APD1 and theamounts of the clock shift on the sender side, stored in the memory 270.FIG. 17B is a diagram schematically showing a data table of the ratiosbetween the photon counts of the photon detectors APD0 and APD1 and theamounts of the clock shift on the receiver side, stored in the memory270. As shown in FIG. 17B, the optical powers output to APD0 and APD1and the amount of the clock shift θ_(j) then made at the receiver 20 areall stored in the memory 270. Therefore, the optimal timing of the clocksignal at the receiver 20 can be determined based on this data. Sincethe determination method is similar to the method in the case of thesender 10 as described with reference to FIG. 11, a description thereofwill be omitted.

The present invention is applicable to optical power measurementequipment in general that measures the optical power in very weakoptical communications. Moreover, the present invention can be appliednot only to plug and play two-way systems as described above, but alsoto one-way quantum cryptographic systems. Furthermore, the applicationof the present invention is not limited to the quantum key distribution,but the present invention is applicable to all the systems and schemesin quantum cryptographic communications.

1. An apparatus for measuring optical power of a series of opticalpulses, comprising: a photon detector for detecting photon arrivalaccording to driving timing having time intervals each corresponding toa constant period of time; a counter for counting a number of photonsdetected by the photon detector; and a measurement section for measuringoptical power of the series of optical pulses from a time average of thenumber of photons counted by the counter in each of the time intervalswhile phase-shifting the driving timing in steps of a predeterminedamount of phase within a predetermined phase range which issubstantially coincident with a period of the optical pulses.
 2. Theapparatus according to claim 1, wherein the measurement section measuresthe optical power of the series of optical pulses based on the number ofphotons obtained for a period of time corresponding to a plurality oftime intervals at the driving timing for each phase shift.
 3. Theapparatus according to claim 1, wherein the measurement sectionsequentially and continuously shifts the driving timing in steps of thepredetermined amount of phase and, when the driving timing has beencompletely shifted over the predetermined phase range, measures theoptical power based on the number of photons counted, and wherein thepredetermined phase range corresponds to 360 degrees.
 4. The apparatusaccording to claim 1, wherein the measurement section sequentiallyshifts the driving timing in steps of the predetermined amount of phaseto store in a memory the number of photons obtained at the drivingtiming for each phase shift and, when the driving timing has beencompletely shifted over the predetermined phase range, measures theoptical power based on the number of photons stored in the memory, andwherein the predetermined phase range corresponds to 360 degrees.
 5. Theapparatus according to claim 1, further comprising a timing controllerfor controlling a phase shift of the driving timing, wherein themeasurement section stores in a memory the number of photons counted bythe counter at the driving timing for each phase shift whilesequentially shifting the driving timing, and measures the optical powerbased on the number of photons stored in the memory.
 6. The apparatusaccording to claim 5, wherein the measurement section sequentiallystores in the memory an amount of phase shift of the driving timing andthe number of photons corresponding to the amount of phase shift.
 7. Theapparatus according to claim 6, wherein the optical power of the seriesof optical pulses is obtained from a total number of photonscorresponding to the amount of phase shift over the predetermined phaserange.
 8. The apparatus according to claim 1, wherein the photondetector is an optoelectronic device to which a bias voltage is appliedaccording to the driving timing, wherein the optoelectronic device candetect an incident photon for a duration of applying the bias voltage.9. The apparatus according to claim 1, wherein each of the opticalpulses is a pulse of very weak light which is 1 photon/pulse or less.10. An optical communication system for transmitting information betweena first communication device and a second communication device through aplurality of communication channels, wherein the first communicationdevice comprises: a modulator for modulating a series of optical pulsesaccording to original information to be transmitted, at given modulationtiming to transmit the series of modulated optical pulses through afirst communication channel; and a timing supplier for supplying themodulation timing to the modulator, wherein the modulation timing ischangeable, and the second communication device comprises: a photondetector for detecting photon arrival of the series of optical pulsesthrough the first communication channel according to driving timinghaving time intervals each corresponding to a constant period of time; acounter for counting a number of photons detected by the photondetector; a measurement section for measuring optical power of theseries of optical pulses from a time average of the number of photonscounted by the counter in each of the time intervals whilephase-shifting the driving timing in steps of a predetermined amount ofphase within a predetermined phase range which is substantiallycoincident with a period of the optical pulses; and a timing controllerfor controlling the modulation timing of the first communication devicethrough a second communication channel based on the optical powermeasured by the measurement section.
 11. The optical communicationsystem according to claim 10, wherein the timing controller monitors theoptical power measured by the measurement section while shifting themodulation timing along time axis, to search for the modulation timingproviding a desired optical power.
 12. An optical receiver forcommunicating with an optical transmitter through a plurality ofcommunication channels, comprising: a photon detector for detectingphoton arrival of a series of optical pulses according to driving timinghaving time intervals each corresponding to a constant period of time,wherein the series of optical pulses is transmitted by the opticaltransmitter through a first communication channel; a counter forcounting a number of photons detected by the photon detector; ameasurement section for measuring optical power of the series of opticalpulses from a time average of the number of photons counted by thecounter in each of the time intervals while phase-shifting the drivingtiming in steps of a predetermined amount of phase within apredetermined phase range which is substantially coincident with aperiod of the optical pulses; and a timing controller for controllingthe modulation timing of the optical transmitter through a secondcommunication channel based on the optical power measured by themeasurement section.
 13. The optical receiver according to claim 12,wherein the photon detector comprises a first photon detector and asecond photon detector, wherein the optical receiver further comprisesan optical modulation state detector for detecting modulation states ofoptical pulses received from the optical transmitter through the firstcommunication channel and outputs its optical detection signal to eitherthe first photon detector or the second photon detector depending ondetected modulation states.
 14. The optical receiver according to claim13, wherein the measurement section calculates a ratio of optical powerseach measured by the first photon detector and the second photondetector, wherein the timing controller controls the modulation timingof the optical transmitter based on the ratio of optical powers.
 15. Amethod for measuring optical power of a series of optical pulses,comprising: shifting driving timing of a photon detector, wherein thedriving timing has time intervals each corresponding to a constantperiod of time; detecting photon arrival of the series of optical pulsesby driving the photon detector according to the driving timing; countinga number of photons detected by the photon detector; and measuringoptical power of the series of optical pulses from a time average of thenumber of photons counted in each of the time intervals whilephase-shifting the driving timing in steps of a predetermined amount ofphase within a predetermined phase range which is substantiallycoincident with a period of the optical pulses.
 16. The method accordingto claim 15, wherein the number of photons is counted for a period oftime corresponding to a plurality of time intervals at the drivingtiming for each phase shift.
 17. The method according to claim 15,wherein by sequentially and continuously shifting the driving timing insteps of the predetermined amount of phase, the optical power ismeasured based on the number of photons obtained when the driving timinghas been completely shifted over the predetermined phase range, andwherein the predetermined phase range corresponds to 360 degrees. 18.The method according to claim 15, wherein by sequentially shifts thedriving timing in steps of the predetermined amount of phase, storing ina memory the number of photons obtained at the driving timing for eachphase shift, wherein when the driving timing has been completely shiftedover the predetermined phase range, the optical power is measured basedon the number of photons stored in the memory.
 19. The method accordingto claim 15, wherein the number of photons counted is stored in a memoryat the driving timing for each phase shift while sequentially shiftingthe driving timing, wherein the optical power is measured based on thenumber of photons stored in the memory.
 20. A computer-readable mediumstoring a computer program for measuring optical power of a series ofoptical pulses, comprising: shifting driving timing of a photondetector, wherein the driving timing has time intervals eachcorresponding to a constant period of time; detecting photon arrival ofthe series of optical pulses by driving the photon detector according tothe driving timing; counting a number of photons detected by the photondetector; and measuring optical power of the series of optical pulsesfrom a time average of the number of photons counted in each of the timeintervals while phase-shifting the driving timing in steps of apredetermined amount of phase within a predetermined phase range whichis substantially coincident with a period of the optical pulses, whereinthe number of photons counted is stored in a memory at the drivingtiming for each phase shift while sequentially shifting the drivingtiming, wherein the optical power is measured from the time average ofthe number of photons stored in the memory.
 21. The apparatus accordingto claim 1, wherein the driving timing is determined at least in partbased on a random number.
 22. The optical communication system accordingto claim 10, wherein the driving timing is determined at least in partbased on a random number.
 23. The computer readable medium according toclaim 20, wherein the driving timing is determined at least in partbased on a random number.
 24. The apparatus according to claim 1,wherein the predetermined amount of phase which is each phase-shiftingstep of the driving timing is shorter than the predetermined phaserange.
 25. The optical communication system according to claim 10,wherein the predetermined amount of phase which is each phase-shiftingstep of the driving timing is shorter than the predetermined phaserange.
 26. The optical receiver according to claim 12, wherein thepredetermined amount of phase which is each phase-shifting step of thedriving timing is shorter than the predetermined phase range.
 27. Themethod according to claim 15, wherein the predetermined amount of phasewhich is each phase-shifting step of the driving timing is shorter thanthe predetermined phase range.
 28. The computer-readable mediumaccording to claim 20, wherein the predetermined amount of phase whichis each phase-shifting step of the driving timing is shorter than thepredetermined phase range.